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The FW method is particularly used in an investment situation where we need to compute the equivalent worth of the project at the end of its investment period.
Primary objective of time value of money methods is to maximise the future wealth of the owners of a firm

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PW method is based on the concept of equivalent worth of all cash flows relative to some base or beginning point in time called the "present".
All cash inflows and outflows are discounted to the present point in time at an interest rate that is generally the MARR.
A positive PW for an investment project is an amount of profit over the minimum amount required by the investors.

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FW Decision rule: If FW (i = MARR) > 0, the project is economically justified.

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To determine the project worthiness, the present equivalent of all cash flows must be computed using MARR as the interest rate. If the present worth is greater than or equal to zero, the project is acceptable.

PW Decision Rule: If PW (i = MARR) > 0, the project is economically justified

To find the PW as a function of i% of a series of cash inflows and outflows, it is necessary to discount future amounts to the present by using the interest rate over the appropriate study period in the following manner (Figure 2):

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The AW of a project is an equal annual series of dollar amounts, for a stated period, that is equivalent to the cash inflows and outflows at an interest rate that is generally the MARR.
Hence, the AW of a project is annual equivalent revenues or savings (R) minus annual equivalent expenses (E) less its annual equivalent capital recovery (CR) amount

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AW Decision Rule:  If AW (i =MARR) > 0, the project is economically justifiedAW (i%) = R – E - CR (i%)

AW of a project is equivalent to its PW and FW.

AW = PW (A/P, i%, N)

AW = FW (A/F, i% , N)

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In PW's example 2, the $110,000, retrofitted space-heating system was projected to save $30,000 per year in electrical power and be worth $8,000 at the end of the six-year study period. Use the FW method to determine whether the project is still economically justified if the system has zero market value after six years. The MARR is 15% per year.

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In this example, we need to find the future equivalent of the $110,000 investment and the $30,000, annual savings at an interest rate of 15% per year.

FW (15%) = -$110,000 (F/P, 15%, 6) + $30,000 (F/A, 15%,6)

=-$110,000 (2.3131) + $30,000 (8.7537)

=$8,170

The heating system is still profitable project (FW > 0) even if it has no market value at the end of the study period.

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The CR amount for a project is the equivalent uniform annual cost of the capital invested. It is an annual amount that covers the following two items:

1. Loss in value asset

2. Interest on invested capital

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Consider a device that will cost $10,000, last five years, and have a salvage (market) value of $2,000. Thus the loss in value of this asset over five years is $8,000. Additionally, the MARR is 10% per year.

CR (i%) = I (A/P, i%, N) – S (A/F, i%, N)

I= Initial Investment

S = Salvage (market) value at the end of the study period

N = project study period.